Developing a Multi-Objective Linear Model for an Optimal Water Allocation Based on Four Bankruptcy Rules and Solve it Through the Fuzzy Compromise Approach

A multi-objective linear optimization model has been formulated, which is used for water and crop area allocation in two irrigation and drainage networks of Dorudzan and Karbal, including five farming regions. The developed model is based on four bankruptcy rules of proportional cutback (PC), constrained equal awards (CEL), constrained equal losses (CEL), and adjusted proportional (APR) in terms of the certainty and uncertainty in the water availability. The developed model has four objective functions to reflect the various agricultural and environmental consumptions and is solved for two dry and non-dry conditions using a fuzzy compromise approach. The outputs of the model showed that the regions with higher shares of water receives the most allocated water through the bankruptcy rules of the PC and CEL in dry and non-dry condition, respectively. On the other hand, the most allocated water for the regions with lower shares of water occurs through the bankruptcy rule of the CEA in both hydro climatic conditions. The outcome of the stability evaluation using the bankruptcy stability index (BASI) indicated that this criterion could not be used to evaluate stability under all bankruptcy situations; thus, one should take the necessary precaution for making a decision according to its output